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social science
introduction to logic

Questions and Answers of Introduction To Logic

For each of the following arguments, construct an indirect proof of validity. (P₁): (NVF) (C.D) (P₂): DDV (P₂): VOI (P): IDA (P): AD ~C ~
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
For each of the following two arguments, construct an indirect proof of validity.If a sharp fall in the prime rate of interest produces a rally in the stock market, then inflation is sure to come
For each of the following arguments, inferring just two statements from the premises will produce a formal proof of its validity. Construct a formal proof for each of these arguments. In these formal
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT. In each case, use the notation in parentheses.If the linguistics investigators are
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, construct an indirect proof of validity. (P₁): RD-M (P₂): RD (~M~S) (P₂):~MD (~S~G) :. RD-G
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.[D ⊃ (F ⊃ G)] ⊃ [(D ⊃ F) ⊃ (D ⊃ G)]
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): A ⊃ (B ⋅ C)(P2): B ⊃ (D ⋅ E)(P3): (A ⊃ D) ⊃ (F ≡ G)(P4): A ⊃ (B
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (I ꓦ ~~ J) ⋅ K2. [~ L ⊃ ~ (K ⋅ J)] ⋅[K ⊃ (I
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Use Conditional Proof (C.P.) to prove that the following statements are tautologies.G ⊃ (H ⊃ G)
If there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations on which, and the number of
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): T ⊃ (U ⋅ V)(P2): U ⊃ (W ⋅ X)(P3): (T ⊃ W) ⊃ (Y ≡ Z)(P4): (T ⊃ U)
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
Use Conditional Proof to prove the validity of the following arguments. G (P₁): (HD) (P₂): (CD) (E > F) (P₂): G (CVE) (P): (DVF) (HVD) :. G = (DVF)
For each of the following arguments, construct an indirect proof of validity. P₁: B [(OV~0) (TVU)] P₂: UD~(GV-G) 2 :. BOT
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
For each of the following arguments, construct an indirect proof of validity. P₁: (FVG) (D. E) P₂: (EVH) DQ 2° P₂: (FVH) ::Q
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (D ⋅ E) ⊃ ~ F2. F ꓦ (G ⋅ H)3. D ≡ E∴ D ⊃ G4.
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): (O ⋅ P) ⊃ (Q ⊃ R)(P2): S ⊃ ~ R(P3): ~ (P ⊃ ~ S)(P4): ~ (O ⊃ Q)∴ ~ O
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
Use Conditional Proof to prove the validity of the following arguments. (P₁): [W] (~X~Y)] · [ZƆ ~ (XVY)] (P₂): (~AW) (~BZ) (P3): (AX) (BY) :. X = Y +
Use Conditional Proof to prove the validity of the following arguments. (P₁): (KL) (P₂): (LVN) :. K = M (MN) {[O (OVP)] (K.M)}
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. A ⊃ B2. B ⊃ C3. C ⊃ A4. A ⊃ ~ C∴ ~ A ⋅ ~ C5. A
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
For each of the following arguments, construct an indirect proof of validity. P: (OVP) P₂: (EVL) P3: (QVZ) ::~0 (D. E) (QV~D) - (O. E)
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): (J ⋅ K) ⊃ (L ⊃ M)(P2): N ⊃ ∼ M(P3): ~ (K ⊃ ∼ N)(P4): ∼ (J ⊃ ~
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. Y ⊃ Z2. Z ⊃ [Y ⊃ (R ꓦ S)]3. R ≡ S4.
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): [(D ꓦ E) ⋅ F] ⊃ G(P2): (F ⊃ G) ⊃ (H ⊃ I)(P3): H∴ D ⊃ I
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. T ⋅ (U ꓦ V)2. T ⊃ [U ⊃ (W ⋅ X)]3. (T ⋅ V) ⊃
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
For each of the following arguments, construct an indirect proof of validity. P₁: DD (ZDY) P₁: ZD (Y-Z) 2° ::~DV~Z)
Use Conditional Proof to prove the validity of the following arguments. (P₁): QV (RS) (P₂): [R (RS)] - (TV U) (UV) (P₂): (TQ) :. QVV .
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
For each of the following, either construct a formal proof of validity or prove invalidity by means of the STTT.(P1): [(X ⋅ Y) ⋅ Z] ⊃ A(P2): (Z ⊃ A) ⊃ (B ⊃ C)(P3): B∴ X ⊃ C
For the following statements, if there are forced truth-value assignments, make them. If there are no forced truth-value assignments, determine, using Maxim V, the requisite truth-value combinations
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
For each numbered statement that is not a premise in each of the formal proofs that follow, state the rule of inference that justifies it.1. (Q ꓦ ~ R) ꓦ S2. ~ Q ꓦ (R ⊃ ~ Q)∴ R ⊃ S3. (~ Q
The following set of arguments involves, in each case, one inference only, in which one of the ten logical equivalences set forth in this section has been employed. Here are two examples, the first
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Translate each of the following into the logical notation of propositional functions and quantifiers, in each case using the abbreviations suggested and making each formula begin with a quantifier,
For each of the following arguments, it is possible to provide a formal proof of validity by validly inferring just three statements. Writing these out, carefully and accurately, will strengthen your
Each of the following exercises presents a flawless formal proof of validity for the indicated argument. For each proof, state the justification for each inferred statement (i.e., each statement that
Here follows a set of twenty elementary valid arguments. They are valid because each of them is exactly in the form of one of the nine elementary valid argument forms. For each of them, state the
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
Using the letters E , I , J , L , and S to abbreviate the simple statements, “Egypt’s food shortage worsens,” “Iran raises the price of oil,” “Jordan requests more U.S. aid,” “Libya
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true? ~ {~[(B · ~ C) ꓦ (Y · ~ Z)] · [(~ B ꓦ X) ꓦ (B ꓦ ~Y )]}
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~ {[(~ A ⋅ B) ⋅ (~ X ⋅ Z)] ⋅ ~ [(A ⋅ ~ B) ꓦ ~ (~ Y · ~ Z)]}
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[A · (B ꓦ C)] · ~[(A · B ) ꓦ (A · C)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[X ꓦ (Y · Z)] ꓦ ~[(X ꓦ Y) · (X ꓦ Z)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?[A ꓦ (B ꓦ C)] · ~[(A ꓦ B) ꓦ C]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~[(A ⋅ B) ꓦ ~(B ⋅ A)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(A ꓦ C)ꓦ ~ (X · ~Y)
Use truth tables to decide which of the following biconditionals are tautologies.[(p ⊃ q) · (q ⊃ p)] ≡ [(p · q) ꓦ (~ p · ~ q)]
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(X V Z) · (~ X V Z)
Symbolize the following, using capital letters to abbreviate the simple statements involved.Chile will call for a meeting of all the Latin American states only if both Argentina mobilizes and Brazil
Use truth tables to decide which of the following biconditionals are tautologies.[(p · q) ⊃ r] = [p ⊃ (q ⊃ r)]
Symbolize the following, using capital letters to abbreviate the simple statements involved.Brazil will protest to the UN only if Argentina mobilizes.
If A, B, and C are true statements and X, Y, and Z are false statements, which of the following are true?~(A ꓦ Y) · (B ꓦ X)

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